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Maximum a Posteriori Estimators as a Limit of Bayes Estimators
Published Web Location
https://arxiv.org/pdf/1611.05917.pdfNo data is associated with this publication.
Abstract
Maximum a posteriori and Bayes estimators are two common methods of point estimation in Bayesian Statistics. A number of references claim that maximum a posteriori estimators are a limiting case of Bayes estimators with 0-1 loss. In this paper, we provide a counterexample which shows that in general this claim is false. We then correct the claim that by providing a level set condition for posterior densities such that the result holds. Since both estimators are defined in terms of optimization problems, the tools of variational analysis find a natural application to Bayesian point estimation.